论文标题
光谱差距和严格的外在性，用于全部紧凑型组在全部因素上的作用
Spectral gap and strict outerness for actions of locally compact groups on full factors
论文作者
论文摘要
我们证明，整个因子$ m $上本地紧凑的组$ g $的外部动作自动严格是外部的，这意味着交叉产品中$ m $的相对通勤者是微不足道的。如果外部自动形态组中的$ g $的图像$ \ operatatorName {out} m $已关闭，我们证明了交叉产品保持满足。我们通过证明在交叉产品中包含$ m $的情况会自动具有光谱间隙属性来获得此结果。在两种情况下，都使用完全不同的方法，仅证明了这种结果仅针对离散组和紧凑型组的作用证明。即使是针对自由小组因素或自由阿拉基木因素的规范性Bogoljubov行动，这些结果也是新的。
We prove that an outer action of a locally compact group $G$ on a full factor $M$ is automatically strictly outer, meaning that the relative commutant of $M$ in the crossed product is trivial. If moreover the image of $G$ in the outer automorphism group $\operatorname{Out} M$ is closed, we prove that the crossed product remains full. We obtain this result by proving that the inclusion of $M$ in the crossed product automatically has a spectral gap property. Such results had only been proven for actions of discrete groups and for actions of compact groups, by using quite different methods in both cases. Even for the canonical Bogoljubov actions on free group factors or free Araki-Woods factors, these results are new.
